Reconciling 2SFCA and i2SFCA via distance decay parameterization

Understanding spatial accessibility and facility crowdedness is central to public service planning, yet existing methods often treat these two metrics separately. The Two-Step Floating Catchment Area (2SFCA) method measures accessibility from the demand side, while the inverted 2SFCA (i2SFCA) assesses crowdedness from the supply side. Without proper integration, these two measures may diverge, raising concerns of their validity. This study introduces a distance decay parameterization framework to reconcile 2SFCA and i2SFCA by optimizing a unified distance decay function through cross-entropy minimization. It demonstrates that aligning demand-side and supply-side flows effectively enforces a behavioral equilibrium between accessibility and crowdedness. A case study using inpatient hospital flow data in Florida shows that the ‘reconciled 2SFCA (r2SFCA) model’ achieves strong alignment between estimated and observed service flows while maintaining simplicity in its formulation. These findings validate the self-organizing nature of human service-seeking behaviors and support a unified, entropy-based calibration strategy for accessibility modeling.